we know that
the unit circle has a radius equals 1 unit
-120°------> is an angle belong to the III quadrant
so
the x and y coordinates will be negative
x=r*cos ∅
y=r*sin ∅
where
r=1
and
∅=180-120-----> ∅=60°
therefore
x=(1)*cos 60°-----> x=1/2-----> x=-1/2 (remember x is negative)
y=(1)*sin 60°-----> y=√3/2-----> y=-√3/2 (remember y is negative
let's apply the Pythagorean theorem
x²+y²-----> (-1/2)²+(-√3/2)²----> (1/4)+(3/4)-----> 1----> is ok because 1 is the radius of the unit circle
the answer is
the coordinates of the terminal point are (-1/2,-√3/2)